Your standard knife. All players start with the knife; they need not explicitly select it, and cannot drop it.

Thompson

The Thompson is the standard rifle for the Allies. Note that despite being the default rifle for the Allies, the Axis can choose it too.

Colt(Allies)

The standard Allied sidearm. All Allies start with this sidearm; it cannot be explicitly chosen.

MP-40

The MP-40 is the standard rifle for the Axis. Note that despite being the default rifle for the Axis, the Allies can choose it too.

Luger(Axis)

The standard Axis sidearm. All Axis start with this sidearm; it cannot be explicitly chosen.

Grenades

Grenades behave as in the usual way: They are thrown, and after a brief delay, they detonate. Unlike in many other first person shooters, grenades in Return to Castle Wolfenstein are very powerful; a single grenade can take out a completely healthy player. Players can "burn off" the timer by holding the attack button down; the seconds tick off.
Grenades are great for clearing fortified positions before a rush.

Sten

The Sten is a silenced weapon, which is helpful when sneaking up behind people, but it doesn't take long for the Sten to overheat (emitting a hissing sound), after which it takes a little while for it to cool down again so it can be fired.
Best when you want to sneak up on people, but there's not a lot of sneaking going on in multiplayer.

Mauser

The Mauser is the standard sniper rifle. When zoomed in, it takes a little while for the sights to settle; firing the gun will jerk the sights up, so it takes some skill. Also, one can only walk (not run) while zoomed in, or one will have to stop looking through the scope.
Best when you want to take out your enemies from a distance.

Panzerfaust

The panzerfaust (German for rocket launcher) is Return to Castle Wolfenstein's rocket launcher. It is very effective, doing significant blast damage wherever it hits, but to compensate it has an extremely slow rate of fire. A panzerfaust soldier is also encumbered, and must move more slowly than other soldiers.
The panzerfaust is best used only briefly at the opening of a campaign to open up some strategic areas; after main areas are breached, the panzerfaust soldier is probably better off switching to a more traditional weapon.

Venom

The Venom is an example of a weapon so powerful it hampers itself. The Venom has a murderous rate of fire, but poor accuracy; furthermore, when it is fired continuously, it quickly overheats (emitting the same hissing sound as the Sten) and has to be held off in order to cool down. Not only that, but it takes time for the barrel to spin up, leading to a significant lag between when the trigger is pulled and bullets start flying. On top of everything else, the Venom soldier must move at a slow pace at all times.
The Venom sounds like a good idea, but in practice it is nearly useless except in very strict defensive positions.

Flamethrower

Everybody's favorite: The Return to Castle Wolfenstein flamethrower was arguably the best flame effect in first person shooters at the point it was released, and long after. The flamethrower is awfully fun to use, but in practice it is not terribly effective and prone to accidental (and sometimes, unfortunately, deliberate) friendly fire. It does a fair amount of damage continuously as the victim is on fire, but perhaps more effectively it obscures the victim's vision (with flames) while they are on fire, which is disorienting and likely to make them unable to effectively retreat.
The flamethrower is most effective in close quarters, defensive fighting indoors at the chokepoints.